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A clock with an iron pendulum keeps correct time at 20 degree celsius ? How much will it lose or gain if temperature changes to 40 degree celsius ? Coefficient of cubical explansion of iron = 36 × 10^-6 degree per celsius Answer is 10.368 seconds please explain?
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A clock with an iron pendulum keeps correct time at 20 degree celsius ...
Solution:
Given: Coefficient of cubical expansion of iron = 36 × 10^-6 /°C
Let the length of the pendulum be L and time period be T at 20°C.
The time period of a simple pendulum is given by the formula:
T = 2π√(L/g)
where g is the acceleration due to gravity.
We know that the acceleration due to gravity is constant and does not depend on temperature.
Therefore, the only variable that changes with temperature is the length of the pendulum.
Let the length of the pendulum at 20°C be L. Then, at 40°C, the length of the pendulum would be:
L' = L(1 + αΔT)
where α is the coefficient of cubical expansion of iron and ΔT is the change in temperature.
ΔT = 40 - 20 = 20°C
Substituting the values, we get:
L' = L(1 + αΔT)
L' = L(1 + 36 × 10^-6 × 20)
L' = L(1 + 0.00072)
L' = 1.00072L
Therefore, the new time period T' at 40°C would be:
T' = 2π√(1.00072L/g)
The difference in time period between 20°C and 40°C is:
ΔT = T' - T
ΔT = 2π(√(1.00072L/g) - √(L/g))
Substituting the values, we get:
ΔT = 2π(√(1.00072L/9.81) - √(L/9.81))
ΔT = 2π(1.00036√(L/9.81) - √(L/9.81))
ΔT = 2π(0.00036√(L/9.81))(L/9.81)
Substituting T = 2π(√(L/9.81)) in the above equation, we get:
ΔT = T × αΔT
ΔT = T × 36 × 10^-6 × 20
ΔT = 0.0072T
Therefore, the clock would lose 0.0072 × T seconds, which is equal to 10.368 seconds (since T = 144 seconds).
Hence, the clock would lose 10.368 seconds if the temperature changes from 20°C to 40°C.
Given: Coefficient of cubical expansion of iron = 36 × 10^-6 /°C
Let the length of the pendulum be L and time period be T at 20°C.
The time period of a simple pendulum is given by the formula:
T = 2π√(L/g)
where g is the acceleration due to gravity.
We know that the acceleration due to gravity is constant and does not depend on temperature.
Therefore, the only variable that changes with temperature is the length of the pendulum.
Let the length of the pendulum at 20°C be L. Then, at 40°C, the length of the pendulum would be:
L' = L(1 + αΔT)
where α is the coefficient of cubical expansion of iron and ΔT is the change in temperature.
ΔT = 40 - 20 = 20°C
Substituting the values, we get:
L' = L(1 + αΔT)
L' = L(1 + 36 × 10^-6 × 20)
L' = L(1 + 0.00072)
L' = 1.00072L
Therefore, the new time period T' at 40°C would be:
T' = 2π√(1.00072L/g)
The difference in time period between 20°C and 40°C is:
ΔT = T' - T
ΔT = 2π(√(1.00072L/g) - √(L/g))
Substituting the values, we get:
ΔT = 2π(√(1.00072L/9.81) - √(L/9.81))
ΔT = 2π(1.00036√(L/9.81) - √(L/9.81))
ΔT = 2π(0.00036√(L/9.81))(L/9.81)
Substituting T = 2π(√(L/9.81)) in the above equation, we get:
ΔT = T × αΔT
ΔT = T × 36 × 10^-6 × 20
ΔT = 0.0072T
Therefore, the clock would lose 0.0072 × T seconds, which is equal to 10.368 seconds (since T = 144 seconds).
Hence, the clock would lose 10.368 seconds if the temperature changes from 20°C to 40°C.
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A clock with an iron pendulum keeps correct time at 20 degree celsius ...
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A clock with an iron pendulum keeps correct time at 20 degree celsius ? How much will it lose or gain if temperature changes to 40 degree celsius ? Coefficient of cubical explansion of iron = 36 × 10^-6 degree per celsius Answer is 10.368 seconds please explain?
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A clock with an iron pendulum keeps correct time at 20 degree celsius ? How much will it lose or gain if temperature changes to 40 degree celsius ? Coefficient of cubical explansion of iron = 36 × 10^-6 degree per celsius Answer is 10.368 seconds please explain? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A clock with an iron pendulum keeps correct time at 20 degree celsius ? How much will it lose or gain if temperature changes to 40 degree celsius ? Coefficient of cubical explansion of iron = 36 × 10^-6 degree per celsius Answer is 10.368 seconds please explain? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A clock with an iron pendulum keeps correct time at 20 degree celsius ? How much will it lose or gain if temperature changes to 40 degree celsius ? Coefficient of cubical explansion of iron = 36 × 10^-6 degree per celsius Answer is 10.368 seconds please explain?.
A clock with an iron pendulum keeps correct time at 20 degree celsius ? How much will it lose or gain if temperature changes to 40 degree celsius ? Coefficient of cubical explansion of iron = 36 × 10^-6 degree per celsius Answer is 10.368 seconds please explain? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A clock with an iron pendulum keeps correct time at 20 degree celsius ? How much will it lose or gain if temperature changes to 40 degree celsius ? Coefficient of cubical explansion of iron = 36 × 10^-6 degree per celsius Answer is 10.368 seconds please explain? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A clock with an iron pendulum keeps correct time at 20 degree celsius ? How much will it lose or gain if temperature changes to 40 degree celsius ? Coefficient of cubical explansion of iron = 36 × 10^-6 degree per celsius Answer is 10.368 seconds please explain?.
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